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Anomalous isotopic symmetry breaking in the $\eta(1405)\tof_0(980)\pi^0\to\pi^+\pi^-\pi^0$ decay through a mechanism featuring anomalousLandau thresholds in the form of logarithmic triangle singularities, i.e.,through the $\eta(1405)\to (K^*\bar K+\bar K^*K)\to(K^+K^-+K^0\bar K^0)\pi^0\tof_0(980)\pi^0 \to\pi^+\pi^- \pi^0$ transition, has been analyzed. It has beenshown that this effect can be correctly quantified only by taking into accountthe nonzero $K^*$ width. Different scales of isotopic symmetry breakingassociated with the $K^+-K^0$ mass difference are compared.

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Isotopic Symmetry Breaking in the $\eta(1405)\to f_0  (980)\pi^0\to\pi^+\pi^-\pi^0$. Decay through a $K\bar K$ Loop Diagram and the  Role of Anomalous Landau Thresholds